B"Suppose there is a h x w grid consisting of empty or full cells. Let's make some definitions: In other words, the i -th row starts exactly with r_i full cells. Similarly, the j -th column starts exactly with c_j full cells. You have values of r and c . Initially, all cells are empty. Find the number of ways to fill grid cells to satisfy values of r and c . Since the answer can be very large, find the answer modulo 1000000007 ,(10^{9} + 7) . In other words, find the remainder after division of the answer by 1000000007 ,(10^{9} + 7) . The first line contains two integers h and w ( 1 <= h, w <= 10^{3} ) -- the height and width of the grid. The second line contains h integers r_{1}, r_{2}, ldots, r_{h} ( 0 <= r_{i} <= w ) -- the values of r . The third line contains w integers c_{1}, c_{2}, ldots, c_{w} ( 0 <= c_{j} <= h ) -- the values of c . Print the answer modulo 1000000007 ,(10^{9} + 7) . In the first example, this is the other possible case. In the second example, it's impossible to make a grid to satisfy such r , c values. In the third example, make sure to print answer modulo (10^9 + 7) . "...